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Appendix I.

757

Fig. 746, shews a tension experiment.    In every case A is the
specimen, B the rotating shaft, and c the load spring,

P. 399. Thick Cylinders.  The stresses within the
material of a thick hollow cyMnder *are really somewhat com-
plicated. They always consist of (i) a radial pressure, greatest
at the inner circumference and decreasing to nothing at the
outer circumference; and (2) a hoop tension, which is greatest
at the inner ring and least at the outer ring, in the manner
shewn in Fig. 352. This diagram shews what the hoop stress
would be in an initially unstrained cylinder.

Now, in order to shew how changes in mechanical construction
can decrease the hoop stress, and therefore decrease the thickness
of cylinder necessary, we will put out of the question the radial corn-
pressive stress and the possible longitudinal tension, and consider
only the hoop stress as tending to break the cylinder. Just as AB,
Fig, 747, is the* diagram of tensile hoop stress, c D is that for the
fluid pressure, or load^ and as A B = c D for conditions of strength.

as with thin cylinders, only that/ is the average hoop stress,

Now, in this diagram it is evident that only the inner rings are
of much value in resisting the load, and the outside rings do not